DETERMINING THE COMPONENT NUMBER OF LINKS CORRESPONDING TO LATTICES

作者：Jin Xian'an^*; Dong Fengming; Tay Eng Guan

来源：Journal of Knot Theory and Its Ramifications, 2009, 18(12): 1711-1726.

DOI：10.1142/S0218216509007671

• Lattice
• medial graph
• component number
• greatest common divisor
• Reidemeister move
• simple closed curve

It is well known that there is a one-to-one correspondence between signed plane graphs and link diagrams via the medial construction. The component number of the corresponding link diagram is however independent of the signs of the plane graph. Determining this number may be one of the first problems in studying links by using graphs. Some works in this aspect have been done. In this paper, we investigate the component number of links corresponding to lattices. Firstly we provide some general results on component number of links. Then, via these results, we proceed to determine the component number of links corresponding to lattices with free or periodic boundary conditions and periodic lattices with one cap (i.e. spiderweb graphs) or two caps.

• 出版日期2009-12
• 单位南阳理工学院; 厦门大学